basic/qdb2023/protocol_mutual.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sys\n",
    "\n",
    "sys.path.append(\"..\")\n",
    "from common_functions import (\n",
    "    encode_message,\n",
    "    decode_message,\n",
    "    create_and_measure_bell_state,\n",
    "    execute_and_extract_results,\n",
    ")\n",
    "from register_manager import RegisterManager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Created classical register register_a with values [1 1 0 1 0]\n",
      "Created classical register register_b with values [1 1 0 0 1]\n",
      "Created classical register register_c with values [1 1 0 1 0]\n",
      "Created classical register register_r with values [0 1 0 1 0]\n",
      "Created quantum register quantum_register with size 10\n"
     ]
    }
   ],
   "source": [
    "# Step 3 - Commitment Exchange: Party B sends commitment to Party A.\n",
    "\n",
    "num_bits = 5\n",
    "\n",
    "# Initialize register manager with classical and quantum registers\n",
    "registers = RegisterManager(\n",
    "    num_classical=4,\n",
    "    num_quantum=1,\n",
    "    size_classical=num_bits,\n",
    "    size_quantum=2 * num_bits,\n",
    "    classical_names=[\"register_a\", \"register_b\", \"register_c\", \"register_r\"],\n",
    "    quantum_names=[\"quantum_register\"],\n",
    ")\n",
    "\n",
    "# Classical registers\n",
    "register_a = registers.get_classical_register(\"register_a\")\n",
    "register_b = registers.get_classical_register(\"register_b\")\n",
    "register_c = registers.get_classical_register(\"register_c\")\n",
    "register_r = registers.get_classical_register(\"register_r\")\n",
    "\n",
    "# Quantum register\n",
    "quantum_register = registers.get_quantum_register(\"quantum_register\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1214.15x1036.78 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 4 - Rapid-bit Exchange: Entangled particle pair generation and half exchange.\n",
    "\n",
    "# Bell state creation and measurement\n",
    "bell_state = create_and_measure_bell_state(num_bits)\n",
    "bell_state.draw(output=\"mpl\", style=\"iqp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measurement Bits: [0, 0, 1, 1, 1]\n",
      "Measurement Prime Bits: [0, 0, 1, 1, 1]\n",
      "Measurement Bits equal Measurement Prime Bits: True\n"
     ]
    }
   ],
   "source": [
    "# Extract results from Bell state measurement\n",
    "measurement_bits, measurement_prime_bits = execute_and_extract_results(bell_state)\n",
    "print(\"Measurement Bits:\", measurement_bits)\n",
    "print(\"Measurement Prime Bits:\", measurement_prime_bits)\n",
    "\n",
    "print(\n",
    "    \"Measurement Bits equal Measurement Prime Bits:\",\n",
    "    np.array_equal(measurement_bits, measurement_prime_bits),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measurement Prime Bits XOR r: [0 1 1 0 1]\n"
     ]
    }
   ],
   "source": [
    "# Party B: XOR operation with the commitment\n",
    "measurement_prime_xor_r = measurement_prime_bits ^ register_r\n",
    "print(\"Measurement Prime Bits XOR r:\", measurement_prime_xor_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Decoded Message at Party A: [0, 1, 1, 0, 1]\n"
     ]
    }
   ],
   "source": [
    "# Step 5 - Measurement and Encoding: Party B measures and encodes the result.\n",
    "\n",
    "# Encoding and decoding messages with register B\n",
    "encoded_message = encode_message(measurement_prime_xor_r, register_b, num_bits)\n",
    "decoded_message_a = decode_message(encoded_message, register_b, num_bits)\n",
    "print(\"\\nDecoded Message at Party A:\", decoded_message_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Conversion to numpy arrays for XOR operations\n",
    "decoded_message_array_a = np.array(decoded_message_a)\n",
    "measurement_bits_array = np.array(measurement_bits)\n",
    "\n",
    "# Party A: XOR operation to obtain r_prime and message encoding\n",
    "r_prime = decoded_message_array_a ^ measurement_bits_array\n",
    "encoded_r_prime_message = encode_message(r_prime, register_c, num_bits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r_prime equals r at Party B: True\n"
     ]
    }
   ],
   "source": [
    "# Step 6 - Reception and XOR: Party A decodes, XORs, and re-encodes the result.\n",
    "\n",
    "# Party B: Decoding r_prime  and comparison\n",
    "decoded_r_prime_b = decode_message(encoded_r_prime_message, register_c, num_bits)\n",
    "print(\"r_prime equals r at Party B:\", np.array_equal(decoded_r_prime_b, register_r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m_bits equals m_prime_bits: True\n"
     ]
    }
   ],
   "source": [
    "# Step 7 - Protocol Finalization: Party A validates the result.\n",
    "\n",
    "# Comparing m_bits with m_prime_bits\n",
    "print(\n",
    "    \"m_bits equals m_prime_bits:\",\n",
    "    np.array_equal(measurement_bits, measurement_prime_bits),\n",
    ")"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
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  "language_info": {
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